Noise in Nonlinear Dynamical Systems: Volume 1, Theory of Continuous Fokker-Planck Systems

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Frank Moss, P. V. E. McClintock
Cambridge University Press, Apr 6, 1989 - Mathematics - 384 pages
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Nature is inherently noisy and nonlinear. It is noisy in the sense that all macroscopic systems are subject to the fluctuations of their environments and also to internal fluctuations. It is nonlinear in the sense that the restoring force on a system displaced from equilibrium does not usually vary linearly with the size of the displacement. To calculate the properties of stochastic (noisy) nonlinear systems is in general extremely difficult, although considerable progress has been made in the past. The three volumes that make up Noise in Nonlinear Dynamical Systems comprise a collection of specially written authoritative reviews on all aspects of the subject, representative of all the major practitioners in the field. The first volume deals with the basic theory of stochastic nonlinear systems. It includes an historical overview of the origins of the field, chapters covering some developed theoretical techniques for the study of coloured noise, and the first English-language translation of the landmark 1933 paper by Pontriagin, Andronov and Vitt.
 

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Contents

Some Markov methods in the theory of stochastic processes
16
Langevin equations with colored noise J m sancho
72
First passage time problems for nonMarkovian processes
110
applica
161
Methods for solving FokkerPlanck equations with applications
191
Macroscopic potentials bifurcations and noise in dissipative
225
Transition phenomena in multidimensional systems models
279
a functional
307
On the statistical treatment of dynamical systems
329
The case of one firstorder equation
337
The case of two firstorder equations
343
Index
349
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